Six hundred of Australia’s biggest private companies could finally be forced to publish their high-level tax information, under a new push by Labor to repair a notorious piece of legislation.

Labor will introduce a private senators’ bill on Monday to amend the Taxation Administration Act 1953, to require private companies with more than $100m in turnover to release their tax information to the public annually.

It allowed 600 of Australia’s biggest private companies to continue to be shielded from public disclosure, because they fell between Labor’s original $100m threshold and the Coalition’s new $200m threshold.

Last month the shadow treasurer, Chris Bowen, signalled Labor would try to reintroduce its 2013 legislation in this term of parliament.

He also said that, if the Senate did not support the legislation, Labor would take its plan to the election.

The shadow assistant treasurer, Andrew Leigh, said the private senators’ bill would restore the level of transparency that was legislated by Labor in government, before it was wound back by the Coalition.

It would also align the threshold for private corporate entities with that of public corporate entities, by lowering the threshold from $200m to $100m.

“It stands alongside other Labor transparency measures, including disclosure of tax haven activity in government tenders, public reporting of country-by-country reports and protection for whistleblowers who…